Physical Sciences and Mathematics Commons^™

The H-Vectors Of Matroids And The Arithmetic Degree Of Squarefree Strongly Stable Ideals, Erik Stokes

University of Kentucky Doctoral Dissertations

Making use of algebraic and combinatorial techniques, we study two topics: the arithmetic degree of squarefree strongly stable ideals and the h-vectors of matroid complexes.

For a squarefree monomial ideal, I, the arithmetic degree of I is the number of facets of the simplicial complex which has I as its Stanley-Reisner ideal. We consider the case when I is squarefree strongly stable, in which case we give an exact formula for the arithmetic degree in terms of the minimal generators of I as well as a lower bound resembling that from the Multiplicity Conjecture. Using this, we can …

Operations In Hilbert Space, Dennis Michael Gumaer

Theses Digitization Project

This thesis reviews some of the major topics in elementary Hilbert space theory. The theory of operators is developed by providing details regarding several types of operators, in particular compact operators. This study of compact operators is the start of the refinement of bounded linear operators to those which are also members of the Schatten p-class operators.

Studies In Free Module And It's Basis, Hsu-Chia Chen

Theses Digitization Project

The purpose of this project was to study some basic properties of free modules over a ring. A module with a basis is called a free module and a free module over a division ring (or field) is called a vector space. We show every vector has a basis and any two bases of a vector space have same cardinality. However, a free module over an arbitrary ring (with identity) does not have this property.

Symmetric Representation Of The Elements Of Finite Groups, Barbara Hope Gwinn-Edwards

Theses Digitization Project

The main purpose of this thesis is to construct finite groups as homomorphic images of infinite semi-direct products.

Estimating Bounds For Nonidentifiale Parameters Using Potential Outcomes, Thidaporn Supapakorn

Doctoral Dissertations

"Conclusions from studies vary regarding the association of weight loss among obese people and measures of health and/or mortality. Total weight loss for individuals in a population may be a combination of intentional weight loss (IWL) and unintentional weight loss (UWL). Among people who have no intention to lose weight, the total weight loss observed is UWL. Among people who have intention to lose weight, the total weight loss is assumed to be UWL and IWL. Note that total weight loss among subjects intending to lose weight is observable but IWL itself is not and, therefore, the latent variable that …

A Numerical Analysis Approach For Estimating The Minimum Traveling Wave Speed For An Autocatalytic Reaction, Erika Blanken

Electronic Theses and Dissertations

This thesis studies the traveling wavefront created by the autocatalytic cubic chemical reaction A + 2B → 3B involving two chemical species A and B, where A is the reactant and B is the auto-catalyst. The diffusion coefficients for A and B are given by DA and DB. These coefficients differ as a result of the chemical species having different size and/or weight. Theoretical results show there exist bounds, v* and v*, depending on DB/DA, where for speeds v ≥ v*, a traveling wave solution exists, while for speeds v < v*, a solution does not exist. Moreover, if DB ≤ DA, and v* and v* are similar to one another and in the order of DB/DA when it is small. On the other hand, when DA ≤ DB there exists a minimum speed vmin, such that there is a traveling wave solution if the speed v > vmin. The determination of vmin is very important in determining …

Fractal Interpolation, Gayatri Ramesh

Electronic Theses and Dissertations

This thesis is devoted to a study about Fractals and Fractal Polynomial Interpolation. Fractal Interpolation is a great topic with many interesting applications, some of which are used in everyday lives such as television, camera, and radio. The thesis is comprised of eight chapters. Chapter one contains a brief introduction and a historical account of fractals. Chapter two is about polynomial interpolation processes such as Newton s, Hermite, and Lagrange. Chapter three focuses on iterated function systems. In this chapter I report results contained in Barnsley s paper, Fractal Functions and Interpolation. I also mention results on iterated function system …

Pseudoquotients: Construction, Applications, And Their Fourier Transform, Mehrdad Khosravi

Electronic Theses and Dissertations

A space of pseudoquotients can be described as a space of either single term quotients (the injective case) or the quotient of sequences (the non-injective case) where the parent sets for the numerator and the denominator satisfy particular conditions. The first part of this project is concerned with the minimal of conditions required to have a well-defined set of pseudoquotients. We continue by adding more structure to our sets and discuss the effect on the resultant pseudoquotient. Pseudoquotients can be thought of as extensions of the parent set for the numerator since they include a natural embedding of that set. …

Degree Of Aproximation Of Hölder Continuous Functions, Benjamin Landon

Electronic Theses and Dissertations

Pratima Sadangi in a Ph.D. thesis submitted to Utkal University proved results on degree of approximation of functions by operators associated with their Fourier series. In this dissertation, we consider degree of approximation of functions in Hα,ρ by different operators. In Chapter 1 we mention basic definitions needed for our work. In Chapter 2 we discuss different methods of summation. In Chapter 3 we define the Hα,ρ metric and present the degree of approximation problem relating to Fourier series and conjugate series of functions in the Hα,ρ metric using Karamata (Κλ) means. In Chapter 4 we present the degree of …

Modeling Transmission Dynamics Of Tuberculosis Including Various Latent Periods, Tracy Atkins

Electronic Theses and Dissertations

The systems of equations created by Blower et al. (1995) and Jia et al. (2007) designed to model the dynamics of Tuberculosis are solved using the computer software SIMULINK. The results are first employed to examine the intrinsic transmission dynamics of the disease through two models developed by Blower et al. (1995). The "simple transmission model" was used primarily to give insight to the behavior of the susceptible, latent, and infectious groups of individuals. Then, we consider a more detailed transmission model which includes several additional factors. This model captures the dynamics of not only the susceptible, latent and infectious …

Comparing Assessment Methods As Predictors Of Student Learning In Undergraduate Mathematics, Nichole Shorter

Electronic Theses and Dissertations

This experiment was designed to determine which assessment method: continuous assessment (in the form of daily in-class quizzes), cumulative assessment (in the form of online homework), or project-based learning, best predicts student learning (dependent upon posttest grades) in an undergraduate mathematics course. Participants included 117 university-level undergraduate freshmen enrolled in a course titled "Mathematics for Calculus". Initially, a multiple regression model was formulated to model the relationship between the predictor variables (the continuous assessment, cumulative assessment, and project scores) versus the outcome variable (the posttest scores). However, due to the possibility of multicollinearity present between the cumulative assessment predictor variable …

Modeling And Synergy Testing Of Drug Combination Data: A Pharmacokinetic Analysis, Jacy Rebecca Crosby

UNF Graduate Theses and Dissertations

In this paper, we present and implement a method to assess the mathematical synergy of two-drug combinations based on a stochastic model. The drugs in question are two isomers that are applied to the human eye via a liquid eye drop. Techniques applied to the data in this paper can be applied to other two-drug combination studies.

We derive the mean and the variance terms of the drug combination "effects" in closed form using Ito's method of stochastic differential equations. The model fit of the data to the individual subject is examined by both statistical and graphical methods. Two estimation …

A Study On The B Family Of Shallow Water Wave Equations, Snehanhsu Saha

Mathematics Dissertations

In this dissertation we study b family of shallow water wave equations which include classical Korteweg-de Vries, Camassa-Holm and Degasperis-Procesi equations. We first establish the models of the Camassa-Holm and Degasperis-Procesi equations, deriving them from the shallow waterwave argument and then compare a large class of properties relating to the two equations. Then we consider the b family equation as the parent equation and derive the above mentioned two equations as special cases of the b-family as well as the classical KdV equation.Next we establish results of local well-posedness using Kato's semigroup theory,global existence and blow up solutions under certain …

Chinese Remainder Theorem And Its Applications, Jacquelyn Ha Lac

Theses Digitization Project

No abstract provided.

Foundations Of Geometry, Lawrence Michael Clarke

Theses Digitization Project

In this paper, a brief introduction to the history, and development of Euclidean geometry will be followed by a biographical background of David Hilbert, highlighting significant events in his educational and professional life. In an attempt to add rigor to the presentation of geometry, Hilbert defined concepts and presented five groups of axioms that were mutually independent yet compatible, including introducing axioms of congruence in order to present displacement.

Factorization, Di Phan Reagan

Theses Digitization Project

The purpose of this thesis will focus on the two most efficient algorithms which are quadratic sieve and number field sieve. Background information such as definitions and theorems are given to help understand the concepts behind each method.

Legendrian Torus Links, Jennifer Dalton

Bryn Mawr College Dissertations and Theses

A basic problem in contact topology is to determine whether two Legendrian knots or links are equivalent. In this dissertation, we will study the equivalence and non-equivalence of Legendrian links that are topologically torus links.

Rigidity And Stability For Isometry Groups In Hyperbolic 4-Space, Youngju Kim

Dissertations, Theses, and Capstone Projects

It is known that a geometrically finite Kleinian group is quasiconformally stable. We prove that this quasiconformal stability cannot be generalized in 4-dimensional hyperbolic space. This is due to the presence of screw parabolic isometries in dimension 4. These isometries are topologically conjugate to strictly parabolic isometries. However, we show that screw parabolic isometries are not quasiconformally conjugate to strictly parabolic isometries. In addition, we show that two screw parabolic isometries are generically not quasiconformally conjugate to each other. We also give some geometric properties of a hyperbolic 4-manifold related to screw parabolic isometries.

A Fuchsian thrice-punctured sphere group has …

Tests For Correlation On Bivariate Nonnormal Distributions, Louanne Margaret Beversdorf

UNF Graduate Theses and Dissertations

Many samples in the real world are very small in size and often do not follow a normal distribution. Existing tests for correlation have restrictions on the distribution of data and sample sizes, therefore the current tests cannot be used in some real world situations.

In this thesis, two tests are considered to test hypotheses about the population correlation coefficient. The tests are based on statistics transformed by a saddlepoint approximation and by Fisher's Z-transformation. The tests are conducted on small samples of bivariate nonnormal data and found to perfom well.

Simulations were run in order to compare the type …

Inverse Limits Of Permutation Maps, Robbie A. Beane

Doctoral Dissertations

"In this paper we study the topological properties of continua which arise as inverse limits on [0; 1] with bonding maps chosen from the permutation family of Markov maps. For such inverse limits, we examine the occurrence of indecomposability, the number of end points in the continuum, and the types of subcontinua present in the continuum. We provide a process for determining the topological structure of the inverse limit generated by a single permutation map, or by the composition of several such maps. Additionally, we show that all such inverse limits are Kelley continua. We will apply these results to …

Modelling Asset Prices Under Regime Switching Diffusions Via First Passage Time, Xiaojing Xi

Theses and Dissertations (Comprehensive)

In this thesis we focus on the development of a new class of stochastic models for asset price processes and their application to option pricing and hedging. The asset price process involves analytical treatments for calculating first-hitting (or first-passage) times for a regular diffusion with killing in combination with Markov state-switching. The dynamics is naturally dictated by the underlying diffusion process itself rather than arising from some addition exogenous process. To date, this class of asset pricing models appears to be novel in the literature and, moreover, offers a significant to the standard geometric Brownian motion commonly used in the …

Dgm-Fd: A Finite Difference Scheme Based On The Discontinuous Galerkin Method, Anne Marguerite Fernando

Mathematics & Statistics Theses & Dissertations

Accurate and efficient numerical wave propagation is important in many areas of study such as computational aero-acoustics (CAA). While dissipation and dispersion errors influence the accuracy of a method, efficiency can be assessed by convergence rates and effective adaptability to different mesh structures. Finite difference and finite element methods are commonly used numerical schemes in CAA. Finite difference methods have the advantages of ease of use as well as high order convergence, but often require a uniform grid, and stable boundary closure can be non-trivial. Finite element methods adapt well to different mesh structures but can become difficult to implement …

Improved Constrained Global Optimization For Estimating Molecular Structure From Atomic Distances, Terri Marie Grant

Mathematics & Statistics Theses & Dissertations

Determination of molecular structure is commonly posed as a nonlinear optimization problem. The objective functions rely on a vast amount of structural data. As a result, the objective functions are most often nonconvex, nonsmooth, and possess many local minima. Furthermore, introduction of additional structural data into the objective function creates barriers in finding the global minimum, causes additional computational issues associated with evaluating the function, and makes physical constraint enforcement intractable. To combat the computational problems associated with standard nonlinear optimization formulations, Williams et al. (2001) proposed an atom-based optimization, referred to as GNOMAD, which complements a simple interatomic distance …